Recent work of [1]} has found that likelihood may not be enough for OOD detection in high-dimensional space. Real samples from a distribution form the area of high probability mass. But a point may have a high density while the surrounding area has a very low density, which indicates the density can change rapidly around it and that point is likely not a sample from the real data distribution. Thus, the norm of gradient of the log-density will be large compared to examples in the area mass. Based on this reasoning, Grathwohl et al. propose a new OOD score: \(\mathbf {\theta }(\mathbf {x})=-\Vert  \frac{\partial \log p_{\mathbf {\theta }}(\mathbf {x})}{\partial \mathbf {x}}\Vert _2\) . Adopting this score function, we find that our model still outperforms the other competing methods (JEM and IGEBM), as shown in Table REF  (bottom).
